It would most certainly not imply that a solo mining pool is a fraud. I'm not sure how you drew that conclusion from this discussion. Is it likely that I will solo mine a block of BTC? Nope. Is it likely I will win the powerball on Wednesday? Nope. Doesn't mean I won't pick up a ticket for a couple bucks and try anyway.
EDIT: It is not a combined effort of shares that solve a block. It is a SINGLE share that does it. Each time you're attempting to find the solution, it either works or it doesn't. Flip a coin. Either it lands on heads or it lands on tails. It can't land on both at the same time. Each flip of that coin has absolutely no relation to the flips before it, or the flips that come after it.
I hear you. Like I said, I'll continue with my reading up on pool mining and bitcoin in general. In the meantime, I'll leave my entire 14GH pointed firmly to the solo mining pool.
PS. In my part of the world, though the lottery jackpot is not always won at each draw, there are always winners in each draw.